Problem: Complete the equation of the line through $(-10,3)$ and $(-8,-8)$. Use exact numbers. $y=$
Explanation: Let's find the slope: $\begin{aligned} \text{Slope}&=\dfrac{-8-3}{-8-(-10)} \\\\ &=\dfrac{-11}{2} \\\\ &=-\dfrac{11}{2} \end{aligned}$ The equation is $y=-\dfrac{11}{2}x+b$ for some $b$. Let's plug the point $({-8},{-8})$ to find $b$ : $\begin{aligned} y&=-\dfrac{11}{2} x+b \\\\ {-8}&=-\dfrac{11}{2}({-8})+b \\\\ -8&=44+b \\\\ -52&=b \end{aligned}$ The equation is $y=-\dfrac{11}{2}x -52$.